To solve this problem, we need to identify the pattern in the given sequences and then apply the same pattern to the options to find the correct one that matches.

Let's examine each set of numbers and the operations performed on them:

1. Sequence 1: 10 - 100 - 50 - 25
   • The operation from 10 to 100 is multiplication by 10: \(10 \times 10 = 100\)
   • The operation from 100 to 50 is division by 2: \(100 \div 2 = 50\)
   • The operation from 50 to 25 is again division by 2: \(50 \div 2 = 25\)
2. Sequence 2: 2 - 4 - 2 - 1
   • The operation from 2 to 4 is multiplication by 2: \(2 \times 2 = 4\)
   • The operation from 4 to 2 is division by 2: \(4 \div 2 = 2\)
   • The operation from 2 to 1 is again division by 2: \(2 \div 2 = 1\)

From these observations, the pattern consists of the following operations:

1. Multiply the first number by 2 (or 10 in the first sequence for an increment operation)
2. Divide by 2
3. Divide by 2 again

Now, we will apply these operations to the options provided and find which option matches the pattern:

1. Option 1: 12 - 144 - 62 - 31
   • 12 to 144: \(12 \times 12 = 144\) (doesn't match the pattern as it exceeds the multiplication factor)
   • 144 to 62: No clear pattern (involving unexpected results)
2. Option 2: 5 - 25 - 15 - 7
   • 5 to 25: \(5 \times 5 = 25\) (does not match the required multiplication factor)
3. Option 3: 4 - 16 - 8 - 4
   • 4 to 16: \(4 \times 4 = 16\) (matches the multiplication by factor = 4)
   • 16 to 8: \(16 \div 2 = 8\) (matches division by factor = 2)
   • 8 to 4: \(8 \div 2 = 4\) (matches division by factor = 2)
4. Option 4: 8 - 64 - 32 - 14
   • 8 to 64: \(8 \times 8 = 64\) (doesn't match as per given pattern)

Therefore, the option 4 - 16 - 8 - 4 matches the defined operations for the given number sequences. Thus, the correct answer is:

Option 3: 4 - 16 - 8 - 4